After I posted that, it started buggin’ me. So….a standard six-stud brick has a volume of 368.64cc. Which, it turns out, is right close to .01 cu ft. Taking your rink ice volume of 4250 cu ft, it would take 425,000 Lego bricks (with a thin layer of ice on top, of course).

Interesting tangent from all this: The original Lego bricks were manufactured in England. Thus, even though they all carry metric dimensions, the numbers come out nice and round and even when converted to English units.